In a small bowl, mix together olive oil, oregano, garlic powder, onion powder, paprika, salt, and pepper. Rub the spice mixture all over the chicken breasts, coating evenly. Let sit for 10 minutes at room temperature, or up to 4 hours refrigerated.
Heat your grill or a large skillet over medium-high heat. If using a skillet, add 1 tsp oil. Cook chicken for 6-8 minutes per side, until internal temperature reaches 165°F and juices run clear. Let rest for 5 minutes, then slice.
For the tzatziki sauce: Grate cucumber and squeeze out as much liquid as possible (about 2-3 tablespoons) using paper towels. In a medium bowl, combine Greek yogurt, grated cucumber, minced garlic, lemon juice, and dill. Season with salt to taste. Refrigerate for at least 30 minutes.
To assemble: Divide the cooled quinoa among 4 bowls. Top with sliced chicken, cucumber, cherry tomatoes, red onion, olives, and feta cheese. Drizzle with tzatziki sauce and serve immediately.
